To predict the principal for the first three years given that it decreases by 4.5% each year, we can calculate the new principal for each year using the formula:
\[ \text{New Principal} = \text{Old Principal} \times (1 - \text{Decrease Rate}) \]
Where the decrease rate is 4.5%, or 0.045. Let's calculate the principal for each year:
Year 1
\[ \text{Principal for Year 1} = 320,000 \times (1 - 0.045) = 320,000 \times 0.955 = 305,600 \]
Year 2
\[ \text{Principal for Year 2} = 305,600 \times (1 - 0.045) = 305,600 \times 0.955 = 291,836 \]
Year 3
\[ \text{Principal for Year 3} = 291,836 \times (1 - 0.045) = 291,836 \times 0.955 = 278,258.28 \]
Now, rounding to the nearest hundredth, we can fill in the table:
| Year | Principal | |------|-------------------| | 0 | $320,000.00 | | 1 | $305,600.00 | | 2 | $291,836.00 | | 3 | $278,258.28 |
So the completed table is:
- Year 1: $305,600.00
- Year 2: $291,836.00
- Year 3: $278,258.28